An equivalent analysis of non-linear flow along rough-walled fractures based on power spectrum and wavelet transform

The classical cubic law deviates from the estimation of the flow rate because of the surface roughness distributed along the fracture surface, which can be decomposed as the primary and the secondary roughness. A piecewise equivalent model is developed to characterise the relationship between primary and secondary roughness and flow rate inside the fracture, setting the fractal dimension 2.0 as the piecewise point. The rough -walled fracture influenced by the primary and secondary roughness is quantitatively evaluated based on the wavelet transform and the power spectrum method. A classification criterion is then proposed to accurately capture the secondary roughness by investigating the non-linear flow behavior along rough-walled fractures using the lattice Boltzmann method. The results found that secondary roughness greatly enhances the flow non-linearity when the fracture fractal dimension exceeds 2.0, while secondary roughness has little effect on non-linear flow behavior with the fracture fractal dimension less than 2.0. The developed piecewise equivalent model shows that the non-linear flow pattern is affected by both fracture primary and secondary roughness. The flow variation along fractures with identical fracture apertures and primary roughness is greatly related to the influence of the secondary roughness. The increase of secondary roughness greatly decreases the hydraulic aperture and the permeability. This work provides an improved equivalent model which can be potentially used in field practices to precisely predict the non-linear flow property by emphasising the great impacts of the secondary roughness.